Let $f \in C^{1} \left( a, b \right)$ be a real function that goes to zero at
the point $\alpha\in (a, b)$. A robust algorithm to find a zero of such a
function can be built joining a low order method, for which global convergence
is guaranteed, with a high order method. The high order method reaches the
zero with a lower number of steps with respect to the low order one, but the
convergence is guaranteed only if the guess is sufficiently close to the zero.
This guess can be computed using the low order method with a coarse tolerance
rate.
